Minimum Operations to Prime

You are given two positive integers s and t. Your task is to transform s into a prime number that is greater than or equal to t using the minimum number of operations. The allowed operations are:

• Add 1
• Subtract 1
• Multiply by 2

You must output the minimum number of operations required. It is guaranteed that a solution exists for all inputs.

Note: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. The transformation should always yield a positive number.

inputFormat

The input consists of two space-separated integers s and t provided via standard input.

Constraints: Both s and t are positive integers.

outputFormat

Output a single integer representing the minimum number of operations required to transform s into a prime number that is greater than or equal to t.

## sample

10 20

3

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